THE RESONATE-AND-FIRE NEURON: TIME DEPENDENT AND FREQUENCY SELECTIVE NEURONS IN NEURAL NETWORKS

The means through which the nervous system perceives its environment is one of the most fascinating questions in contemporary science. Our endeavors to comprehend the principles of neural science provide an instance of how biological processes may inspire novel methods in mathematical modeling and engineering. The application ofmathematical models towards understanding neural signals and systems represents a vibrant field of research that has spanned over half a century. During this period, multiple approaches to neuronal modeling have been adopted, and each approach is adept at elucidating a specific aspect of nervous system function. Thus while bio-physical models have strived to comprehend the dynamics of actual physical processes occurring within a nerve cell, the phenomenological approach has conceived models that relate the ionic properties of nerve cells to transitions in neural activity. Further-more, the field of neural networks has endeavored to explore how distributed parallel processing systems may become capable of storing memory. Through this project, we strive to explore how some of the insights gained from biophysical neuronal modeling may be incorporated within the field of neural net-works. We specifically study the capabilities of a simple neural model, the Resonate-and-Fire (RAF) neuron, whose derivation is inspired by biophysical neural modeling. While reflecting further biological plausibility, the RAF neuron is also analytically tractable, and thus may be implemented within neural networks. In the following thesis, we provide a brief overview of the different approaches that have been adopted towards comprehending the properties of nerve cells, along with the framework under which our specific neuron model relates to the field of neuronal modeling. Subsequently, we explore some of the time-dependent neurocomputational capabilities of the RAF neuron, and we utilize the model to classify logic gates, and solve the classic XOR problem. Finally we explore how the resonate-and-fire neuron may be implemented within neural networks, and how such a network could be adapted through the temporal backpropagation algorithm.

The GABAB1b isoform mediates long-lasting inhibition of dendritic Ca2+ spikes in layer 5 somatosensory pyramidal neurons

The apical tuft of layer 5 pyramidal neurons is innervated by a large number of inhibitory inputs with unknown functions. Here, we studied the functional consequences and underlying molecular mechanisms of apical inhibition on dendritic spike activity. Extracellular stimulation of layer 1, during blockade of glutamatergic transmission, inhibited the dendritic Ca2+ spike for up to 400 ms. Activation of metabotropic GABAB receptors was responsible for a gradual and long-lasting inhibitory effect, whereas GABAA receptors mediated a short-lasting (approximately 150 ms) inhibition. Our results suggest that the mechanism underlying the GABAB inhibition of Ca2+ spikes involves direct blockade of dendritic Ca2+ channels. By using knockout mice for the two predominant GABAB1 isoforms, GABAB1a and GABAB1b, we showed that postsynaptic inhibition of Ca2+ spikes is mediated by GABAB1b, whereas presynaptic inhibition of GABA release is mediated by GABAB1a. We conclude that the molecular subtypes of GABAB receptors play strategically different physiological roles in neocortical neurons.